How to get smoke to pour out object holes?
It looks like the resolution you are using for the smoke domain is too coarse. This makes the size of a smoke voxel possibly comparable or bigger than the apertures, preventing the smoke to "see" that they are there. By increasing it to 64 I've managed to see the smoke escape from both eyes. 



To make sure that the smoke would come out within the time frame (I've done a test bake of 170 frames), I've also increased the time scaling factor, and I've added a starting normal velocity to the Flow object.

I'm not sure whether it counts, but I've also changed the obstacle type to "Animated" (doing this alone isn't enough, you'll still need to increase the resolution)